Tsallis Entropy In Bi-level And Multi-level Image Thresholding

Tsallis Entropy In Bi-level And Multi-level Image Thresholding

Loading document ...
Loading page ...


Author(s): Amelia Carolina Sparavigna

Download Full PDF Read Complete Article

DOI: 10.18483/ijSci.613 537 1289 40-49 Volume 4 - Jan 2015


The maximum entropy principle has a relevant role in image processing, in particular for thresholding and image segmentation. Different entropic formulations are available to this purpose; one of them is based on the Tsallis non-extensive entropy. Here, we propose a discussion of its use for bi- and multi-level thresholding.


Image Processing, Tsallis Entropy, Thresholding


  1. Tsallis, C. (1988). Possible Generalization of Boltzmann-Gibbs Statistics. Journal of Statistical Physics, 52, 479-487
  2. Tsallis, C. (2009). Nonadditive Entropy and Nonextensive Statistical Mechanics - an Overview after 20 Years. Braz. J. Phys, 39, 337-35
  3. Djerou, L., Khelil, N., Dehimi, N.H., & Batouche, M. (2012). Automatic Multi-Level Thresholding Segmentation Based on Multi-Objective Optimization. Journal of Applied Computer Science & Mathematics, 13 (6), 24-31
  4. Renyi, A. (1970). Probability Theory. North-Holland, Amsterdam
  5. Maszczyk, T., & Duch, W. (2008). Comparison of Shannon, Renyi and Tsallis Entropy Used in Decision Trees. Artificial Intelligence and Soft Computing - ICAISC 2008, 643-651, Springer Berlin Heidelberg
  6. Havrda, J., & Charvát, F., (1967). Quantification Methods of Classification Processes: Concept of Structural Alpha-Entropy. Kybernetica (Prague) 3, 95-100
  7. Sahoo, P.K., & Arora, G. (2006). Image Thresholding Using Two-Dimensional Tsallis– Havrda– Charvát. Pattern Recognition Letters, 27, 520-528
  8. Gull, S.F., & Skilling, J. (1984). Maximum Entropy Method in Image Processing. Communications, Radar and Signal Processing, IEE Proceedings F, 131(6), 646-659
  9. Yamano, T. (2001). Information Theory Based in Nonadditive Information Content. Entropy 3, 280–292; Yamano, T. (2000). arXiv:cond-mat/0010074 [cond-mat.stat-mech]
  10. Portes de Albuquerque, M., Esquef, I.A., Gesualdi Mello, A.R., & Portes de Albuquerque, M. (2004). Image Thresholding Using Tsallis Entropy. Pattern Recognition Letters, 25(9), 1059-1065
  11. Sezgin, M., & Sankur, B. (2004). Survey over Image Thresholding Techniques and Quantitative Performance Evaluation. Journal of Electronic Imaging, 13(1), 146-165
  12. Kapur, J.N., Sahoo, P.K., & Wong, A.K.C. (1985). A New Method for Gray-Level Picture Thresholding Using the Entropy of the Histogram. Comput. Vision Graphics Image Process., 29, 273-285
  13. Shitong Wang, & Chung, F.L. (2005). Note on the Equivalence Relationship between Renyi-Entropy Based and Tsallis-Entropy Based Image Thresholding. Pattern Recognition Letters, 26(14), 2309-2312
  14. Sahoo, P., Wilkins, C., & Yeager, J. (1997). Thresholding Selection Using Renyi’s Entropy. Pattern Recognition, 30 (1), 71–84
  15. Sahoo, P.K., & Arora, G. (2004). A Thresholding Method Based on Two Dimensional Renyi’s Entropy. Pattern Recognition, 37 (6), 1149-1161
  16. Sparavigna, A. (2009). The Digital Restoration of Da Vinci's Sketches. arXiv:0903.1448 [cs.CV]
  17. Sparavigna, A.C. (2011). An Image Processing of a Raphael's Portrait of Leonardo. arXiv:1111.6030 [cs.CV]
  18. Sparavigna, A.C. (2011). Portraits of Leonardo da Vinci. Archaeogate, 6 December 1011
  19. Sathya, P. D., & Kayalvizhi, R. (2010). PSO-based Tsallis Thresholding Selection Procedure for Image Segmentation. International Journal of Computer Applications, 5(4), 39-46
  20. Yudong Zhang, & Lenan Wu, Optimal Multi-Level Thresholding Based on Maximum Tsallis Entropy via an Artificial Bee Colony Approach. Entropy 2011, 13(4), 841-859
  21. Tamalika Chaira (2015). Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques. CRC Press
  22. Shi Weili, Miao Yu, Chen Zhanfang, & Zhang Hongbiao (2009). Research of Automatic Medical Image Segmentation Algorithm Based on Tsallis Entropy and Improved PCNN. International Conference on Mechatronics and Automation, ICMA 9-12 August 2009, 1004-1008
  23. Yudong Zhang, & Lenan Wu (2008). Pattern Recognition via PCNN and Tsallis Entropy. Sensors, 8(11), 7518-7529
  24. El-Sayed, M.A., Abdel-Khalek, S. & Abdel-Aziz, E. (2011). Study of Efficient Technique Based on 2D Tsallis Entropy for Image Thresholding. International Journal on Computer Science and Engineering (IJCSE), 3(9), 3125-3138
  25. Ramirez-Villegas, J.F., & Ramirez-Moreno, D.F. (2012). Wavelet Packet Energy, Tsallis Entropy and Statistical Parameterization for Support Vector-Based and Neural-Based Classification of Mammographic Regions. Neurocomputing, 77(1), 82–100
  26. El-Sayed, M.A. (2011). A New Algorithm Based Entropic Threshold for Edge Detection in Images. IJCSI - International Journal of Computer Science Issues, 8(5), 71-78
  27. Khader, M. & Ben Hamza, A. (2012). An Information- Theoretic Method for Multimodality Medical Image Registration. Expert Systems with Applications, 39(5), 5548-5556
  28. Fabbri, R., Gonçalves, W.N., Lopes, F.J.P., & Bruno, O.M. (2012). Multi-q Pattern Analysis: A Case Study in Image Classification, Physica A: Statistical Mechanics and its Applications, 391(19), 4487-4496

Cite this Article:

International Journal of Sciences is Open Access Journal.
This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Author(s) retain the copyrights of this article, though, publication rights are with Alkhaer Publications.

Search Articles

Issue June 2023

Volume 12, June 2023

Table of Contents

World-wide Delivery is FREE

Share this Issue with Friends:

Submit your Paper